In (3+1)d at least there are 8 Pin groups depending on P^2=±1, T^2=±1, (PT)^2=±1; not all are compatible with GR.
As described in https://arxiv.org/pdf/1709.02742.pdf the ones compatible with GR have P^2T^2=-1 and (PT)^2=1 while the ones coming out of usual Clifford algebra constructions have P^2=T^2 and (PT)^2=-1.
In (3+1)d at least there are 8 Pin groups depending on P^2=±1, T^2=±1, (PT)^2=±1; not all are compatible with GR. As described in https://arxiv.org/pdf/1709.02742.pdf the ones compatible with GR have P^2T^2=-1 and (PT)^2=1 while the ones coming out of usual Clifford algebra constructions have P^2=T^2 and (PT)^2=-1.